IT HARDLY SEEMS possible that only a little less than three months ago Israel's Prime Minister Menachem Begin and Egypt's President Anwar Sadat were hugging and carrying on in the Congressional Gallery and at the White House in celebration of the Camp David accords. "Let us pledge to make the spirit of Camp David a new chapter in the history of our nations," said Mr. Sadat. "Peace now celebrates a great victory for the nations of Egypt and Israel and for all mankind," said Mr. Begin. The two had already promised each other to complete an Israeli-Egyptian peace treaty within three months. Smiling confidently, Mr. Sadat nodded his acceptance of Mr. Begin's spirited challenge to finish the job ahead of schedule.

Fine words, no doubt sincerely meant at the time. But the deadline for an Egyptian-Israeli peace treaty is now but a short week away, and the "spirit of Camp David" is almost nowhere in evidence. Instead, for some weeks, as President Carter rightly noted in his breakfast conference on Thursday, "there have been unwarranted delays, quibbling over what seem to us to be insignificant language differences, and excessive public statements on both sides that have made the negotiating process excessively difficult." It is not necessary here to review all the bidding, or the bickering, to which Mr. Carter was referring, and still less to recite the solid and substantial progress that has been made. The point is that enough impressive obstacles to an agreement have been thrown up by both sides -- the Israelis' loud and gratuitous insistence on the right to expand their West Bank settlements, the quarrel over "target dates" for self-government on the West Bank, new Egyptian demands to renegotiate key articles of a treaty draft that had once seemed mutually acceptable -- to raise genuine doubts among even the most optimistic Americans about a negotiating process whose success they once saw as inevitable.

The question now is almost too painful to ask: Is it possible that the Camp David accords did in fact impose upon both Israel and Egypt commitments to larger concessions than they now feel, with the experience of almost three months of hard bargaining behind them, that they can safely make? The crude manner of Mr. Begin's handling of the touchy settlements aside, it cannot be denied that the internal political strains upon him are enormous. And if Mr. Sadat's performance has been erratic and inconsistent, it must also be conceded that the Baghdad conference and the intense hostility of some of his Arab antagonists, not to mention the deep distrust of even those Arabs he would count among his allies, have placed him under increasing pressure to hang tough. The hard fact, in short, is that nobody in Washington is prepared to say at this stage whether the issues still unresolved reflect a growing willingness on both sides to accept all the risks of standing pat, or are merely a part of familiar tactical maneuvering, susceptible to resolution by American mediation.

It is the answer to that question, rather than any quick fix, that Secretary of State Cyrus Vance will be seeking as he sets off today for Cairo and presumably, later in the week, to Jerusalem. It might be too much to picture this mission in terms of make-or-break. But both the Israelis and the Egyptians, we suspect, would be seriously mistaken in any belief that they can safely give a back of the hand to Mr. Vance with confidence that Mr. Carter himself can somehow be counted on to step in and revive that old Camp David magic.

The president could ultimately take a personal hand in defining the terms and reconciling the differences having to do with that part of the Camp David accords bearing on the so-called linkage between an Egyptian-Israeli agreement and the longer, harder process of providing some form of automony and self-determination for the West Bank Palestinians. For Mr. Carter, in a real sense, is the custodian of those wider accords.

But the terms of the Egytian-Israeli peace treaty itself are for the parties themselves to resolve. Dec. 17 was their deadline. As a practical matter, with time fast running out, that deadline may now have to be extended, as Secretary Vance now seems to be suggesting. But this is not something to be done casually, or without extracting some new commitments that a new deadline would be met. We cannot agree with the relaxed Israeli view, as expressed by Israel's ambassador to Washington, Simcha Dinitz, when he indicated the other day that nothing would be lost "if we don't reach agreement by a certain date." On the contrary, we think the president was absloutely right at his Thursday press conference when he said, "If we go past Dec. 17, 1 think it would cast doubts on whether the Egyptians and Israelis would carry out the difficult terms of the upcoming peace treaty." If firm deadlines are allowed to slide by, future deadlines lose their credibility. And if that happens, not just a peace treaty between Israel and Egypt, but also the far larger aims and accomplishments of Camp David will be put dangerously at risk.